The Lindblad approach to open quantum systems is introduced to study t
he dynamics of a single trapped ion prepared in nonclassical motional
states and subjected to continuous measurement of its internal populat
ion. This results in an inhibition of the dynamics similar to the one
occurring in the quantum Zeno effect. In particular, modifications to
the Jaynes-Cummings collapses and revivals arising from an initial coh
erent state of motion in various regimes of interaction with the drivi
ng laser; are dealt with in detail.